1. Linear Discriminant Analysis(LDA)
Name: Po-Shen Kuo
Instructor: Dr. Longin Jan Latecki

2. Introduction
The primary purpose of LDA is to separate samples of distinct groups by transforming then to a space which maximises their between-class separability while minimising their within-class variability.

3. Method Let the between-class scatter matrix Sb be defined as
and the within-class scatter matrix Sw be defined as

4. Method
It has been shown that Plda is in fact the solution of the following eigensystem problem:

5. Method
the Fisher’s criterion is maximised when the projection matrix Plda is composed of the eigenvectors of
with at most (g-1) nonzero corresponding eigenvalues.

6. Method The LDA is an axis projection.
Once the projection is found all the data points can be transformed to the new axis system along with the class means and covariances.

7. Conclusion